In [[mathematics]], [[physics]], and [[engineering]], '''spatial frequency''' is a characteristic of any structure that is periodic across position in space. The spatial frequency is a measure of how often the structure repeats per unit of distance. The [[SI]] unit of spatial frequency is [[cycles]] per [[meter]]. In [[image processing]] applications, the spatial frequency often is measured as lines per [[millimeter]], which is 1000 times smaller than the SI unit.

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'''Spatial frequency''' is a characteristic of any structure that is periodic across position in space. The spatial frequency is a measure of how often the structure repeats per unit of distance. The [[SI]] unit of spatial frequency is cycles per meter.

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In wave mechanics, the spatial frequency <math>\nu \ </math> is related to the wavelength <math> \lambda \ </math> by

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In [[wave mechanics]], the spatial frequency <math>\nu \ </math> is related to the wavelength <math> \lambda \ </math> by

:<math>\nu \ = \ { 1 \over \lambda } </math>

:<math>\nu \ = \ { 1 \over \lambda } </math>

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Likewise, the [[wave number]] ''k'' is related to spatial frequency and wavelength by

Likewise, the [[wave number]] ''k'' is related to spatial frequency and wavelength by

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:<math> k \ = \ 2 \pi \nu \ = \ { 2 \pi \over \lambda } </math>

:<math> k \ = \ 2 \pi \nu \ = \ { 2 \pi \over \lambda } </math>

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===Visual perception===

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==Visual perception==

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In the study of [[visual perception]], [[sine wave|sinusoidal gratings]] are frequently used to probe the capabilities of the visual system. In these stimuli, spatial frequency is expressed as the number of [[cycles]] per [[degree (angle)|degree]] of [[visual angle]].

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In the study of [[visual perception]], [[sine wave|sinusoidal]][[grating]]s are frequently used to probe the capabilities of the visual system. In these stimuli, spatial frequency is expressed as the number of cycles per [[degree (angle)|degree]] of [[visual angle]].<br />

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Different spatial frequencies convey different information about the appearance of a stimulus. High spatial frequencies represent abrupt spatial changes in the image, such as edges, and generally correspond to configural information and fine detail. Low spatial frequencies, on the other hand, represent global information about the shape, such as general orientation and proportions.<ref>{{cite journal |author=Bar M |title=Visual objects in context |journal=Nat. Rev. Neurosci. |volume=5 |issue=8 |pages=617–29 |year=2004 |month=Aug |pmid=15263892 |doi=10.1038/nrn1476 |quote=<br/>[http://www.nature.com/nrn/journal/v5/n8/box/nrn1476_BX2.html Box 2: Spatial frequencies and the information they convey] }}</ref>

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In the general population of adults, the threshold for spatial frequency discrimination is about 7%. It is often poorer in dyslexic individuals <ref>{{cite journal |author=Ben-Yehudah G, Ahissar M |title=Sequential spatial frequency discrimination is consistently impaired among adult dyslexics |journal=Vision Res. |volume=44 |issue=10 |pages=1047–63 |year=2004 |month=May |pmid=15031099 |doi=10.1016/j.visres.2003.12.001 }}</ref>.

Spatial frequency is a characteristic of any structure that is periodic across position in space. The spatial frequency is a measure of how often the structure repeats per unit of distance. The SI unit of spatial frequency is cycles per meter.

In wave mechanics, the spatial frequency is related to the wavelength by

Likewise, the wave numberk is related to spatial frequency and wavelength by

In the study of visual perception, sinusoidalgratings are frequently used to probe the capabilities of the visual system. In these stimuli, spatial frequency is expressed as the number of cycles per degree of visual angle.
Different spatial frequencies convey different information about the appearance of a stimulus. High spatial frequencies represent abrupt spatial changes in the image, such as edges, and generally correspond to configural information and fine detail. Low spatial frequencies, on the other hand, represent global information about the shape, such as general orientation and proportions.[1]
In the general population of adults, the threshold for spatial frequency discrimination is about 7%. It is often poorer in dyslexic individuals [2].